# General Solution of the Luneberg Lens Problem

@article{Morgan1958GeneralSO, title={General Solution of the Luneberg Lens Problem}, author={Samuel P. Morgan}, journal={Journal of Applied Physics}, year={1958}, volume={29}, pages={1358-1368} }

The general solution is obtained for the index of refraction of a variable‐index, spherical lens which will form perfect geometrical images of the points of two given concentric spheres on each other. One conjugate sphere is assumed to be outside the lens or at its surface, while the other may be either inside, outside, or at the surface. If one of the spheres is of infinite radius, the lens will focus a parallel beam perfectly at a point on the other sphere.It is shown that the index of…

## 168 Citations

A solution to the complement of the generalized Luneburg lens problem

- PhysicsCommunications Physics
- 2021

Lenses are of interest for the design of directive antennas and multi-optics instruments in the microwave, terahertz and optical domains. Here, we introduce an optical problem defined as the…

Surface-wave luneberg lens antennas

- Physics
- 1960

It is demonstrated that a surface-wave structure having isotropy in the plane of the structure can be operated as a lens. The index of refraction is given for a dielectric slab on a ground plane, a…

Improvements in the computation of refractive-index profiles for the generalized Luneburg lens

- Physics
- 1991

The generalized Luneburg lens problem has been reexamined with the aim of optimizing the methods for computing the Luneburg integral, which determines the refractive-index distribution of spherically…

Microwave heating of a Luneberg lens

- Physics
- 1964

A calculation is made of the maximum steady-state temperature rise due to a small amount of dielectric dissipation in a Luneberg lens which is continuously illuminated by a powerful microwave…

Gradient-index Geodesic Lenses for Integrated Optics: A Uniform Theory

- Physics
- 1988

Abstract A new generation of planar waveguide lenses for integrated-optical circuits is proposed. They have potentially perfect focusing capabilities due to the assumed simultaneous action of the…

Algorithm for lens calculations in the geometrized Maxwell theory

- Computer Science, PhysicsSaratov Fall Meeting
- 2018

The work of the proposed algorithm in the framework of geometrized approach to optics for solving the problem of finding the propagation path of the electromagnetic radiation depending on environmental parameters is demonstrated.

General solution of the non-full-aperture Luneburg lens problem

- Physics
- 1983

The generalized Luneburg lens problem has been redefined to include non-full-aperture lenses, and as a result a new class of solutions has been made possible. A particular solution is obtained for…

Comparison of luneburg lens antennas made from homogeneous material

- Physics2018 Ural Symposium on Biomedical Engineering, Radioelectronics and Information Technology (USBEREIT)
- 2018

In this article a comparison is made of the cylindrical Luneburg lens of inhomogeneous dielectric filling with the lens made from the material with a constant value of the dielectric permittivity…

Scattering by spherically stratified microwave lens antennas

- Physics
- 1994

A comprehensive treatment of scattering by sources in the region of a spherically stratified object composed of discrete shells is presented and compared with measured results. The work encompasses…

Internal‐Field Characteristics of Spherical Particles

- Physics, Geology
- 1995

The finely stratified sphere model was used to calculate electromagnetic fields inside homogeneous and radially inhomogeneous spheres which are illuminated by electromagnetic plane waves. A complete…

## References

SHOWING 1-4 OF 4 REFERENCES

The impossibility of certain desirable luneberg lens modifications

- PhysicsIRE Transactions on Antennas and Propagation
- 1956

THE DIFFICULTY of rapid scanning over the outer surface of a Luneberg lens has led Gutman1 to devise a lens in which the feed moves on a smaller radius. In Gutman's lens the feed horn points toward…

Modified Luneberg Lens

- Physics
- 1954

Spherically symmetric optical instruments, and their desirability for microwaves, are discussed. Application of Hamiltonian optics in analyzing the rays in the Luneberg lens has led to formula of a…